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Chapter 1 The Art of Problem Solving © 2008 Pearson Addison-Wesley.
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Chapter 1: The Art of Problem Solving
1.1 Solving Problems by Inductive Reasoning 1.2 An Application of Inductive Reasoning: Number Patterns 1.3 Strategies for Problem Solving 1.4 Calculating, Estimating, and Reading Graphs © 2008 Pearson Addison-Wesley. All rights reserved
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Chapter 1 Section 1-2 An Application of Inductive Reasoning: Number Patterns © 2008 Pearson Addison-Wesley. All rights reserved
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An Application of Inductive Reasoning: Number Patterns
Number Sequences Successive Differences Number Patterns and Sum Formulas Figurate Numbers © 2008 Pearson Addison-Wesley. All rights reserved
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© 2008 Pearson Addison-Wesley. All rights reserved
Number Sequences Number Sequence A list of numbers having a first number, a second number, and so on, called the terms of the sequence. Arithmetic Sequence A sequence that has a common difference between successive terms. Geometric Sequence A sequence that has a common ratio between successive terms. © 2008 Pearson Addison-Wesley. All rights reserved
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Successive Differences
Process to determine the next term of a sequence using subtraction to find a common difference. © 2008 Pearson Addison-Wesley. All rights reserved
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Example: Successive Differences
Use the method of successive differences to find the next number in the sequence. 14, 22, 32, 44,... Find differences Find differences 58 14 2 Build up to next term: 58 © 2008 Pearson Addison-Wesley. All rights reserved
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Number Patterns and Sum Formulas
Sum of the First n Odd Counting Numbers If n is any counting number, then Special Sum Formulas For any counting number n, © 2008 Pearson Addison-Wesley. All rights reserved
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© 2008 Pearson Addison-Wesley. All rights reserved
Example: Sum Formula Use a sum formula to find the sum Solution Use the formula with n = 48: © 2008 Pearson Addison-Wesley. All rights reserved
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© 2008 Pearson Addison-Wesley. All rights reserved
Figurate Numbers © 2008 Pearson Addison-Wesley. All rights reserved
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Formulas for Triangular, Square, and Pentagonal Numbers
For any natural number n, © 2008 Pearson Addison-Wesley. All rights reserved
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Example: Figurate Numbers
Use a formula to find the sixth pentagonal number Solution Use the formula with n = 6: © 2008 Pearson Addison-Wesley. All rights reserved
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